Reduced basis approximations of structural displacements for optimaldesign

A new solution procedure for improved approximate reanalyses of structures, using results of a single precise analysis, is presented. The proposed procedure is based on combining the computed terms of a series expansion, used as high-quality basis vectors, with coefficients of a reduced basis expression. The latter coefficients can readily be determined for each trial design by various criteria. The results are measured by the errors in satisfying the analysis equations and are compared in terms of the quality of the approximations. The proposed approach is suitable for various types of design variables and can be used with a general finite element model. A general reanalysis procedure is introduced and the physical significance of first-order approximations is demonstrated. Several numerical examples illustrate the effectiveness of the solution process. It is shown that high-quality approximations of displacements can be obtained with a small computational effort for very large changes in the design variables.